Section 3.6 - 3.7

LONGITUDINAL

CHANGES IN CG

_.

Consider a ship floating on an even keel, that is, no list or trim...

ww_.

When a weight, w, is added, it causes a change draft.

w_.

The ship will pivot about the center of flotation, F.

F

Tfwd

The change in draft will be evident in a change of draft forward...

Taft

…and aft.

Trim

The difference between the fore and aft drafts is the change in trim:

Trim = Taft - Tfwd

Graphically, it looks like this. First, the ship is represented with a line representing its initial state:

O)( _.F

FPAP

You can simulate this on your paper by turning the sheet in the direction that thebow or stern would sink because of the added weight, then drawing a line to represent the new position.

As weight is added, the the ship rotates about F:

w

O)(F

_.AP FP

wO)(F

_.

Now, rotate the sheet so that the line drawn becomes level and acts as the new waterline:

wO)(F

_.

Tfwd

Taft

Trim

The changes in draft can now be read directly…

Taft is below the WL, so it’s subtracted. Tfwd is above the waterline, so it’s added to the draft.

FPAP

There are two aspects of draft to consider when finding the change in draft:

1. Change in draft due to the parallel sinkage of the vessel due to the added weight, “w”:

TPS = w TPI

2. Change in draft due to the moment created by the added weight at a distance from F, or “wl”:

Trim = wl MT1”

Tfwd new = Tfwd old TPS Trim

AND

Taft new = Taft old TPS Trim

These two measurements- change due to parallel sinkage andchange in trim due to moment- when added with the initial draft will give you the TOTAL draft, forward and aft:

Trim = wl MT1”

TPS = w TPI

Let’s consider change due to the parallel sinkage of the vessel first:

TPS = w TPI

TPI, Tons Per Inch Immersion is a geometric function of the vessel at a given draft and is taken from the Curves of Form

• The added weight, w, will cause the vessel to “sink” a small distance for the length of the entire vessel

• We assume that the weight is applied at F! This assures that the sinkageis uniform over the length of the ship

Now consider the change in trim due to the created moment of the added weight:

Trim = wl MT1”

MT1”, or the Moment to Trim 1”, is also from the Curves of Form

• The weight, w, at a distance, l, from the center of flotation, F, creates a moment that causes the ship to rotate about F

• This rotation causes one end to sink and the other end to rise

• The degree of rise or fall depends on the location of F with regard to the entire length of the ship as given by Lpp

The value for Trim will be for the entire length of the ship:

Trim = wl MT1”

...Now we need to find how much of the trim is aft and how much is forward!

wO)(F

_.

Tfwd

Taft

Trim

l

Lpp

To find the trim distribution, consider the similar triangles formed below:

The largest triangle shows the TOTAL change in trim, Trim

The hatched green triangle shows the forward trim Tfwd

The hatched yellow area triangle shows the aft trim, Taft

wO)(F

_.

Tfwd

Taft

Trim

l

Lpp

daft dfwd

For these similar triangles there is a ratio aspect that relates to each:

TrimLpp

Taft

daft

Tfwd

dfwd

= =

(The short leg divided by the long leg of the triangle!)

wO)(F

_.

Tfwd

Taft

Trim

l

Lpp

daft dfwd

Tfwd new = Tfwd old TPS T

AND

Taft new = Taft old TPS T

Knowing how to find the change in draft from parallel sinkage and from thecreated moment, you can now find the total change in draft fore and aft:

GIVEN:

Lpp = 101.7 ft Draft = (10.5 + 10.1)/2 = 10.3ft

amidships = 50.85 ft s = 2LT x 215 = 430LT

LCF = 51.5 ft from FP, or .65ft aft of amidships

DRAW A PICTURE!

Example:

The YP floats at a draft 10.5 ft aft and 10.1ft forward. A load of 10LT is placed15ft forward of amidships. Find the final forward and aft drafts.

101.7

Daft = 50.2 Dfwd = 51.5

)(_. Taft

Tfwd TrimF

O 10LT

15

Step 1: Find change due to parallel sinkage

TPS = w TPI

TPS = 10LT 235 x .02LT/in

TPS = 2.13in

101.7

Daft = 50.2 Dfwd = 51.5

)(_. Taft

Tfwd TrimF

O 10LT

15

Step 2: Find change due to moment

Trim = wl MT1”

Trim = 10LT x 15ft 252.5 x .141 LT-ft/in

Trim = 4.21in

101.7

Daft = 50.2 Dfwd = 51.5

)(_. Taft

Tfwd TrimF

O 10LT

15

Step 3: Divide the Trim based on similar triangles

TrimLpp

Taft

daft

Tfwd

dfwd

= =

4.21in

101.7ft

Taft

50.2ft

Tfwd

51.5ft= =

4.21in

101.7ftTaft 50.2ft x= 2.08 in=

4.21in

101.7ftTfw

d

51.5ft x= 2.13 in=

101.7

Daft = 50.2 Dfwd = 51.5

)(_. Taft

Tfwd TrimF

O 10LT

15

Step 4: Sum the changes in draft fore and aft

Forward:

Tfwd new = Tfwd old TPS Tmoment

Tfwd new = 10.1ft + (2.13in + 2.13in) x (1ft/12in)

Tfwd new = 10.1ft + .36ft

Tfwd new = 10.46ft

101.7

Daft = 50.2 Dfwd = 51.5

)(_. Taft

Tfwd TrimF

O 10LT

15

Step 4: Sum the changes in draft fore and aft

Aft:

Taft new = Taft old TPS Tmoment

Taft new = 10.5ft + (2.13in - 2.08in) x (1ft/12in)

Taft new = 10.5ft + .004ft

Taft new = 10.504ft

101.7

Daft = 50.2 Dfwd = 51.5

)(_. Taft

Tfwd TrimF

O 10LT

15